Ah, ok. So it sounds like your goal is to play a multiclass character, and you envisioned the character as a Barbarian first and then thought Fighter would be a good combination with it. In that case, I think getting levels of both classes under your belt quickly would be a high priority so you get to experience a multiclass character right out the gate. Maybe in that case, start with Barbarian and switch to Fighter right away. Maybe something Barbarian 1, Fighter 1-5 or 1-6, then back to Barbarian for 2-4, then Fighter up to 11, and finally Barbarian up to 9, if the game lasts that long. That would end up delaying your first ASI and Extra Attack, but only for 1 level. Again, it’s all about what your priorities are.